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- Title
Homogenization of Nonlinear Degenerate Non-monotone Elliptic Operators in Domains Perforated with Tiny Holes.
- Authors
Woukeng, Jean Louis
- Abstract
The paper deals with the homogenization problem beyond the periodic setting, for a degenerated nonlinear non-monotone elliptic type operator on a perforated domain Ω in ℝ with isolated holes. While the space variable in the coefficients a and a is scaled with size ε ( ε>0 a small parameter), the system of holes is scaled with ε size, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The homogenization problem is formulated in terms of the general, so-called deterministic homogenization theory combining real homogenization algebras with the Σ -convergence method. We present a new approach based on the Besicovitch type spaces to solve deterministic homogenization problems, and we obtain a very general abstract homogenization results. We then illustrate this abstract setting by providing some concrete applications of these results to, e.g., the periodic homogenization, the almost periodic homogenization, and others.
- Subjects
ASYMPTOTIC homogenization; ELLIPTIC operators; STOCHASTIC convergence; ALGEBRAIC spaces; MONOTONE operators
- Publication
Acta Applicandae Mathematicae, 2010, Vol 112, Issue 1, p35
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-009-9552-z